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Why no solution to 3 eqns. in 3 unk. ?

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  • Subject: [mg5037] Why no solution to 3 eqns. in 3 unk. ?
  • From: "Christopher R. Carlen" <crobc at>
  • Date: Sat, 19 Oct 1996 16:40:37 -0400
  • Organization:
  • Sender: owner-wri-mathgroup at

Recently I tried to solve this system:

 -a x   + b   + c y z == 0
 -a x z + b z - c y   == 0
  a     + b   - c     == 0

for the variables, {x, y, z} .

Well, Mathematica fails to give two of the solutions that I get by 
hand, which are:

 x = -1
 y = i
 z = i


 x = -1
 y = -i
 z = -i

Mathematica does give the solution:

 x = (c - a)/a
 y = 0

which is a valid solution.  But why does it not give the other two 
solutions ?

Obviously, this system is odd, so if anyone can characterize it, or 
explain what this all means, I'd appreciate it.

This system arose in determining the constants of Schroedinger's 
equation, from basic quantum mechanics.  I have simplified the 
problem to a generic case that behaves in the same manner as the 
actual physical problem.

Christopher R. Carlen
crobc at
carlenc at

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